A backward driving assist apparatus for a vehicle may include: a vehicle speed sensor configured to measure a vehicle speed by counting a wheel pulse of a wheel; a steering angle sensor configured to measure a steering angle of a steering wheel; a yaw rate sensor configured to measure a yaw rate of the vehicle during driving; a driving trace storage configured to store driving trace data generated during forward driving; and a controller configured to estimate the position of the ego vehicle, interpolate the driving trace data generated at each preset distance, store the driving trace data in the driving trace storage, read the driving trace data from the driving trace storage during backward driving, generate a target steering angle by compensating for a direction angle error from the ego vehicle position, and output the target steering angle to an MDPS controller.